IntegratedGaussianPRF#
- class photutils.psf.IntegratedGaussianPRF(*, flux=1, x_0=0, y_0=0, sigma=1, bbox_factor=5.5, **kwargs)[source]#
Bases:
CircularGaussianSigmaPRF
Deprecated since version 2.0.0: The IntegratedGaussianPRF class is deprecated and may be removed in a future version. Use
CircularGaussianSigmaPRF
orCircularGaussianPRF
instead.A circular 2D Gaussian PSF model integrated over pixels.
This model is evaluated by integrating the 2D Gaussian over the input coordinate pixels, and is equivalent to assuming the PSF is 2D Gaussian at a sub-pixel level. Because it is integrated over pixels, this model is considered a PRF instead of a PSF.
The Gaussian is normalized such that the analytical integral over the entire 2D plane is equal to the total flux.
This model is equivalent to
CircularGaussianPRF
, but it is parameterized in terms of the standard deviation (sigma) instead of the full width at half maximum (FWHM).- Parameters:
- fluxfloat, optional
Total integrated flux over the entire PSF.
- x_0float, optional
Position of the peak in x direction.
- y_0float, optional
Position of the peak in y direction.
- sigmafloat, optional
Width of the Gaussian PSF.
- bbox_factorfloat, optional
The multiple of the standard deviation (sigma) used to define the bounding box limits.
- **kwargsdict, optional
Additional optional keyword arguments to be passed to the
astropy.modeling.Model
parent class.
See also
Notes
The circular Gaussian function is defined as:
\[f(x, y) = \frac{F}{4} \left[ {\rm erf} \left(\frac{x - x_0 + 0.5} {\sqrt{2} \sigma} \right) - {\rm erf} \left(\frac{x - x_0 - 0.5} {\sqrt{2} \sigma} \right) \right] \left[ {\rm erf} \left(\frac{y - y_0 + 0.5} {\sqrt{2} \sigma} \right) - {\rm erf} \left(\frac{y - y_0 - 0.5} {\sqrt{2} \sigma} \right) \right]\]where \(F\) is the total integrated flux, \((x_{0}, y_{0})\) is the position of the peak, \(\sigma\) is the standard deviation of the Gaussian, and \({\rm erf}\) denotes the error function.
The model is normalized such that:
\[\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} f(x, y) \,dx \,dy = F\]References
Deprecated since version 2.0.0: The IntegratedGaussianPRF class is deprecated and may be removed in a future version. Use
CircularGaussianSigmaPRF
orCircularGaussianPRF
instead.Attributes Summary
The peak amplitude of the Gaussian.
A
tuple
of lengthn_inputs
defining the bounding box limits, or raiseNotImplementedError
for no bounding_box.A
dict
mapping parameter names to their upper and lower bounds as(min, max)
tuples or[min, max]
lists.Fitter should set covariance matrix, if available.
List of parameter equality constraints.
Function (similar to the model's
evaluate
) to compute the derivatives of the model with respect to its parameters, for use by fitting algorithms.A
dict
mapping parameter names to their fixed constraint.Gaussian FWHM.
A flag indicating whether or not a custom bounding_box has been assigned to this model by a user, via assignment to
model.bounding_box
.A flag indicating whether or not a custom inverse model has been assigned to this model by a user, via assignment to
model.inverse
.List of parameter inequality constraints.
The input units of the model.
Allow dimensionless input (and corresponding output).
Enforce strict units on inputs to evaluate.
Returns a new
Model
instance which performs the inverse transform, if an analytic inverse is defined for this model.A dict-like object to store optional information.
Primarily for informational purposes, these are the types of constraints that constrain model evaluation.
The index of the model set axis--that is the axis of a parameter array that pertains to which model a parameter value pertains to--as specified when the model was initialized.
The number of inputs.
The number of outputs.
Return the number of components in a single model, which is obviously 1.
User-provided name for this model instance.
Names of the parameters that describe models of this type.
Return parameters as a pset.
Primarily for informational purposes, these are the types of constraints that can be set on a model's parameters.
A flattened array of all parameter values in all parameter sets.
This property is used to indicate what units or sets of units the output of evaluate should be in, and returns a dictionary mapping outputs to units (or
None
if any units are accepted).A flag indicating whether a model is separable.
Standard deviation of parameters, if covariance matrix is available.
This is a boolean property that indicates whether or not accessing constraints automatically check the constituent models current values.
A
dict
mapping parameter names to their tied constraint.True if this model has been created with
Quantity
objects or if there are no parameters.Methods Summary
__call__
(*inputs[, model_set_axis, ...])Evaluate this model using the given input(s) and the parameter values that were specified when the model was instantiated.
coerce_units
([input_units, return_units, ...])Attach units to this (unitless) model.
copy
()Return a copy of this model.
deepcopy
()Return a deep copy of this model.
evaluate
(x, y, flux, x_0, y_0, sigma)Calculate the value of the 2D Gaussian model at the input coordinates for the given model parameters.
get_bounding_box
([with_bbox])Return the
bounding_box
of a model if it exists orNone
otherwise.Returns True if the model has an analytic or user inverse defined.
input_shape
(inputs)Get input shape for bounding_box evaluation.
output_units
(**kwargs)Return a dictionary of output units for this model given a dictionary of fitting inputs and outputs.
prepare_inputs
(*inputs[, model_set_axis, ...])This method is used in
__call__
to ensure that all the inputs to the model can be broadcast into compatible shapes (if one or both of them are input as arrays), particularly if there are more than one parameter sets.prepare_outputs
(broadcasted_shapes, ...)rename
([name, inputs, outputs])Return a copy of this model with a new name.
render
([out, coords])Evaluate a model at fixed positions, respecting the
bounding_box
.set_slice_args
(*args)sum_of_implicit_terms
(*args, **kwargs)Evaluate the sum of any implicit model terms on some input variables.
with_units_from_data
(**kwargs)Return an instance of the model which has units for which the parameter values are compatible with the data units specified.
without_units_for_data
(**kwargs)Return an instance of the model for which the parameter values have been converted to the right units for the data, then the units have been stripped away.
Attributes Documentation
- amplitude#
The peak amplitude of the Gaussian.
- bbox_with_units#
- bounding_box#
A
tuple
of lengthn_inputs
defining the bounding box limits, or raiseNotImplementedError
for no bounding_box.The default limits are given by a
bounding_box
property or method defined in the class body of a specific model. If not defined then this property just raisesNotImplementedError
by default (but may be assigned a custom value by a user).bounding_box
can be set manually to an array-like object of shape(model.n_inputs, 2)
. For further usage, see Efficient Model Rendering with Bounding BoxesThe limits are ordered according to the
numpy
'C'
indexing convention, and are the reverse of the model input order, e.g. for inputs('x', 'y', 'z')
,bounding_box
is defined:for 1D:
(x_low, x_high)
for 2D:
((y_low, y_high), (x_low, x_high))
for 3D:
((z_low, z_high), (y_low, y_high), (x_low, x_high))
Examples
Setting the
bounding_box
limits for a 1D and 2D model:>>> from astropy.modeling.models import Gaussian1D, Gaussian2D >>> model_1d = Gaussian1D() >>> model_2d = Gaussian2D(x_stddev=1, y_stddev=1) >>> model_1d.bounding_box = (-5, 5) >>> model_2d.bounding_box = ((-6, 6), (-5, 5))
Setting the bounding_box limits for a user-defined 3D
custom_model
:>>> from astropy.modeling.models import custom_model >>> def const3d(x, y, z, amp=1): ... return amp ... >>> Const3D = custom_model(const3d) >>> model_3d = Const3D() >>> model_3d.bounding_box = ((-6, 6), (-5, 5), (-4, 4))
To reset
bounding_box
to its default limits just delete the user-defined value–this will reset it back to the default defined on the class:>>> del model_1d.bounding_box
To disable the bounding box entirely (including the default), set
bounding_box
toNone
:>>> model_1d.bounding_box = None >>> model_1d.bounding_box Traceback (most recent call last): NotImplementedError: No bounding box is defined for this model (note: the bounding box was explicitly disabled for this model; use `del model.bounding_box` to restore the default bounding box, if one is defined for this model).
- bounds#
A
dict
mapping parameter names to their upper and lower bounds as(min, max)
tuples or[min, max]
lists.
- col_fit_deriv = True#
- cov_matrix#
Fitter should set covariance matrix, if available.
- eqcons#
List of parameter equality constraints.
- fit_deriv = None#
Function (similar to the model’s
evaluate
) to compute the derivatives of the model with respect to its parameters, for use by fitting algorithms. In other words, this computes the Jacobian matrix with respect to the model’s parameters.
- fittable = True#
- fixed#
A
dict
mapping parameter names to their fixed constraint.
- flux = Parameter('flux', value=1.0)#
- fwhm#
Gaussian FWHM.
- has_user_bounding_box#
A flag indicating whether or not a custom bounding_box has been assigned to this model by a user, via assignment to
model.bounding_box
.
- has_user_inverse#
A flag indicating whether or not a custom inverse model has been assigned to this model by a user, via assignment to
model.inverse
.
- ineqcons#
List of parameter inequality constraints.
- input_units#
The input units of the model.
- input_units_allow_dimensionless#
Allow dimensionless input (and corresponding output). If this is True, input values to evaluate will gain the units specified in input_units. If this is a dictionary then it should map input name to a bool to allow dimensionless numbers for that input. Only has an effect if input_units is defined.
- input_units_equivalencies = None#
- input_units_strict#
Enforce strict units on inputs to evaluate. If this is set to True, input values to evaluate will be in the exact units specified by input_units. If the input quantities are convertible to input_units, they are converted. If this is a dictionary then it should map input name to a bool to set strict input units for that parameter.
- inputs#
- inverse#
Returns a new
Model
instance which performs the inverse transform, if an analytic inverse is defined for this model.Even on models that don’t have an inverse defined, this property can be set with a manually-defined inverse, such a pre-computed or experimentally determined inverse (often given as a
PolynomialModel
, but not by requirement).A custom inverse can be deleted with
del model.inverse
. In this case the model’s inverse is reset to its default, if a default exists (otherwise the default is to raiseNotImplementedError
).Note to authors of
Model
subclasses: To define an inverse for a model simply override this property to return the appropriate model representing the inverse. The machinery that will make the inverse manually-overridable is added automatically by the base class.
- linear = False#
- meta = None#
A dict-like object to store optional information.
- model_constraints = ('eqcons', 'ineqcons')#
Primarily for informational purposes, these are the types of constraints that constrain model evaluation.
- model_set_axis#
The index of the model set axis–that is the axis of a parameter array that pertains to which model a parameter value pertains to–as specified when the model was initialized.
See the documentation on Model Sets for more details.
- n_inputs = 2#
The number of inputs.
- n_outputs = 1#
The number of outputs.
- n_submodels#
Return the number of components in a single model, which is obviously 1.
- name#
User-provided name for this model instance.
- outputs#
- param_names = ('flux', 'x_0', 'y_0', 'sigma')#
Names of the parameters that describe models of this type.
The parameters in this tuple are in the same order they should be passed in when initializing a model of a specific type. Some types of models, such as polynomial models, have a different number of parameters depending on some other property of the model, such as the degree.
When defining a custom model class the value of this attribute is automatically set by the
Parameter
attributes defined in the class body.
- param_sets#
Return parameters as a pset.
This is a list with one item per parameter set, which is an array of that parameter’s values across all parameter sets, with the last axis associated with the parameter set.
- parameter_constraints = ('fixed', 'tied', 'bounds')#
Primarily for informational purposes, these are the types of constraints that can be set on a model’s parameters.
- parameters#
A flattened array of all parameter values in all parameter sets.
Fittable parameters maintain this list and fitters modify it.
- return_units#
This property is used to indicate what units or sets of units the output of evaluate should be in, and returns a dictionary mapping outputs to units (or
None
if any units are accepted).Model sub-classes can also use function annotations in evaluate to indicate valid output units, in which case this property should not be overridden since it will return the return units based on the annotations.
- separable#
A flag indicating whether a model is separable.
- sigma = Parameter('sigma', value=1.0, fixed=True, bounds=(1.1754943508222875e-38, None))#
- standard_broadcasting = True#
- stds#
Standard deviation of parameters, if covariance matrix is available.
- sync_constraints#
This is a boolean property that indicates whether or not accessing constraints automatically check the constituent models current values. It defaults to True on creation of a model, but for fitting purposes it should be set to False for performance reasons.
- tied#
A
dict
mapping parameter names to their tied constraint.
- uses_quantity#
True if this model has been created with
Quantity
objects or if there are no parameters.This can be used to determine if this model should be evaluated with
Quantity
or regular floats.
- x_0 = Parameter('x_0', value=0.0)#
- y_0 = Parameter('y_0', value=0.0)#
Methods Documentation
- __call__(*inputs, model_set_axis=None, with_bounding_box=False, fill_value=nan, equivalencies=None, inputs_map=None, **new_inputs)#
Evaluate this model using the given input(s) and the parameter values that were specified when the model was instantiated.
- coerce_units(input_units=None, return_units=None, input_units_equivalencies=None, input_units_allow_dimensionless=False)#
Attach units to this (unitless) model.
- Parameters:
- input_unitsdict or tuple, optional
Input units to attach. If dict, each key is the name of a model input, and the value is the unit to attach. If tuple, the elements are units to attach in order corresponding to
Model.inputs
.- return_unitsdict or tuple, optional
Output units to attach. If dict, each key is the name of a model output, and the value is the unit to attach. If tuple, the elements are units to attach in order corresponding to
Model.outputs
.- input_units_equivalenciesdict, optional
Default equivalencies to apply to input values. If set, this should be a dictionary where each key is a string that corresponds to one of the model inputs.
- input_units_allow_dimensionlessbool or dict, optional
Allow dimensionless input. If this is True, input values to evaluate will gain the units specified in input_units. If this is a dictionary then it should map input name to a bool to allow dimensionless numbers for that input.
- Returns:
CompoundModel
A
CompoundModel
composed of the current model plusUnitsMapping
model(s) that attach the units.
- Raises:
- ValueError
If the current model already has units.
Examples
Wrapping a unitless model to require and convert units:
>>> from astropy.modeling.models import Polynomial1D >>> from astropy import units as u >>> poly = Polynomial1D(1, c0=1, c1=2) >>> model = poly.coerce_units((u.m,), (u.s,)) >>> model(u.Quantity(10, u.m)) <Quantity 21. s> >>> model(u.Quantity(1000, u.cm)) <Quantity 21. s> >>> model(u.Quantity(10, u.cm)) <Quantity 1.2 s>
Wrapping a unitless model but still permitting unitless input:
>>> from astropy.modeling.models import Polynomial1D >>> from astropy import units as u >>> poly = Polynomial1D(1, c0=1, c1=2) >>> model = poly.coerce_units((u.m,), (u.s,), input_units_allow_dimensionless=True) >>> model(u.Quantity(10, u.m)) <Quantity 21. s> >>> model(10) <Quantity 21. s>
- copy()#
Return a copy of this model.
Uses a deep copy so that all model attributes, including parameter values, are copied as well.
- deepcopy()#
Return a deep copy of this model.
- evaluate(x, y, flux, x_0, y_0, sigma)#
Calculate the value of the 2D Gaussian model at the input coordinates for the given model parameters.
- Parameters:
- x, yfloat or array_like
The coordinates at which to evaluate the model.
- fluxfloat
The total flux of the star.
- x_0, y_0float
The position of the star.
- sigmafloat
The width of the Gaussian PRF.
- Returns:
- evaluated_model
ndarray
The evaluated model.
- evaluated_model
- get_bounding_box(with_bbox=True)#
Return the
bounding_box
of a model if it exists orNone
otherwise.- Parameters:
- with_bbox
The value of the
with_bounding_box
keyword argument when calling the model. Default isTrue
for usage when looking up the model’sbounding_box
without risk of error.
- has_inverse()#
Returns True if the model has an analytic or user inverse defined.
- input_shape(inputs)#
Get input shape for bounding_box evaluation.
- output_units(**kwargs)#
Return a dictionary of output units for this model given a dictionary of fitting inputs and outputs.
The input and output Quantity objects should be given as keyword arguments.
Notes
This method is needed in order to be able to fit models with units in the parameters, since we need to temporarily strip away the units from the model during the fitting (which might be done by e.g. scipy functions).
This method will force extra model evaluations, which maybe computationally expensive. To avoid this, one can add a return_units property to the model, see return_units.
- prepare_inputs(*inputs, model_set_axis=None, equivalencies=None, **kwargs)#
This method is used in
__call__
to ensure that all the inputs to the model can be broadcast into compatible shapes (if one or both of them are input as arrays), particularly if there are more than one parameter sets. This also makes sure that (if applicable) the units of the input will be compatible with the evaluate method.
- prepare_outputs(broadcasted_shapes, *outputs, **kwargs)#
- classmethod rename(name=None, inputs=None, outputs=None)#
Return a copy of this model with a new name.
- render(out=None, coords=None)#
Evaluate a model at fixed positions, respecting the
bounding_box
.The key difference relative to evaluating the model directly is that this method is limited to a bounding box if the
Model.bounding_box
attribute is set.- Parameters:
- out
numpy.ndarray
, optional An array that the evaluated model will be added to. If this is not given (or given as
None
), a new array will be created.- coordsarray-like, optional
An array to be used to translate from the model’s input coordinates to the
out
array. It should have the property thatself(coords)
yields the same shape asout
. Ifout
is not specified,coords
will be used to determine the shape of the returned array. If this is not provided (or None), the model will be evaluated on a grid determined byModel.bounding_box
.
- out
- Returns:
- out
numpy.ndarray
The model added to
out
ifout
is notNone
, or else a new array from evaluating the model overcoords
. Ifout
andcoords
are bothNone
, the returned array is limited to theModel.bounding_box
limits. IfModel.bounding_box
isNone
,arr
orcoords
must be passed.
- out
- Raises:
- ValueError
If
coords
are not given and theModel.bounding_box
of this model is not set.
Examples
- set_slice_args(*args)#
- strip_units_from_tree()#
- sum_of_implicit_terms(*args, **kwargs)#
Evaluate the sum of any implicit model terms on some input variables. This includes any fixed terms used in evaluating a linear model that do not have corresponding parameters exposed to the user. The prototypical case is
astropy.modeling.functional_models.Shift
, which corresponds to a function y = a + bx, where b=1 is intrinsically fixed by the type of model, such that sum_of_implicit_terms(x) == x. This method is needed by linear fitters to correct the dependent variable for the implicit term(s) when solving for the remaining terms (ie. a = y - bx).
- with_units_from_data(**kwargs)#
Return an instance of the model which has units for which the parameter values are compatible with the data units specified.
The input and output Quantity objects should be given as keyword arguments.
Notes
This method is needed in order to be able to fit models with units in the parameters, since we need to temporarily strip away the units from the model during the fitting (which might be done by e.g. scipy functions).
The units that the parameters will gain are not necessarily the units of the input data, but are derived from them. Model subclasses that want fitting to work in the presence of quantities need to define a
_parameter_units_for_data_units
method that takes the input and output units (as two dictionaries) and returns a dictionary giving the target units for each parameter.
- without_units_for_data(**kwargs)#
Return an instance of the model for which the parameter values have been converted to the right units for the data, then the units have been stripped away.
The input and output Quantity objects should be given as keyword arguments.
Notes
This method is needed in order to be able to fit models with units in the parameters, since we need to temporarily strip away the units from the model during the fitting (which might be done by e.g. scipy functions).
The units that the parameters should be converted to are not necessarily the units of the input data, but are derived from them. Model subclasses that want fitting to work in the presence of quantities need to define a
_parameter_units_for_data_units
method that takes the input and output units (as two dictionaries) and returns a dictionary giving the target units for each parameter.